Formal Verification and Synthesis for Discrete-Time Stochastic Systems

Lahijanian, Morteza; Andersson, Sean B.; Belta, Călin

doi:10.1109/tac.2015.2398883

Cited by 123 publications

(145 citation statements)

References 36 publications

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“…In Case Study 1-2-3 (Sec. 4.1-4.3), we look at the special instance from [21], where the dynamics are autonomous (no actions) and linear: here T x is…”

Section: Remarkmentioning

confidence: 99%

“…Formal verification and strategy synthesis over shs are in general not decidable [4,28], and can be tackled via quantitative finite abstractions. These are precise approximations that come in two main different flavours: abstractions into mdp [4,26] and into imdp [21]. Once the finite abstractions are obtained, and with focus on specifications expressed in (non-nested) pctl or fragments of ltl [5], formal verification or strategy synthesis can be performed via probabilistic model checking tools, such as prism [20], storm [11], iscasMc [16].…”

Section: Formal Verification and Strategy Synthesis Via Abstractionsmentioning

confidence: 99%

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StocHy - automated verification and synthesis of stochastic processes

Cauchi

Abate

2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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StocHy is a software tool for the quantitative analysis of discrete-time stochastic hybrid systems (shs). StocHy accepts a high-level description of stochastic models and constructs an equivalent shs model. The tool allows to (i) simulate the shs evolution over a given time horizon; and to automatically construct formal abstractions of the shs. Abstractions are then employed for (ii) formal verification or (iii) control (policy, strategy) synthesis. StocHy allows for modular modelling, and has separate simulation, verification and synthesis engines, which are implemented as independent libraries. This allows for libraries to be easily used and for extensions to be easily built. The tool is implemented in c++ and employs manipulations based on vector calculus, the use of sparse matrices, the symbolic construction of probabilistic kernels, and multi-threading. Experiments show StocHy's markedly improved performance when compared to existing abstraction-based approaches: in particular, StocHy beats state-of-the-art tools in terms of precision (abstraction error) and computational effort, and finally attains scalability to large-sized models (12 continuous dimensions).

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“…In Case Study 1-2-3 (Sec. 4.1-4.3), we look at the special instance from [21], where the dynamics are autonomous (no actions) and linear: here T x is…”

Section: Remarkmentioning

confidence: 99%

Section: Formal Verification and Strategy Synthesis Via Abstractionsmentioning

confidence: 99%

StocHy - automated verification and synthesis of stochastic processes

Cauchi

Abate

2019

Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control

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“…Consequently, computing P I (Q i |= φ ) and P I (Q i |= φ ) amounts to finding the product Markov Chains induced by I ⊗ A that respectively minimize and maximize the probability of reaching an accepting state. Such reachability problems in IMCs have already been studied and solved when the destination states are fixed for all induced Markov Chains [9] [10]. However, the set of accepting and nonaccepting states may not be fixed in product IMCs and varies as a function of the assumed values for each transition.…”

Section: Problem Formulationmentioning

confidence: 99%

Satisfiability Bounds for co-regular Properties in Interval-valued Markov Chains

Dutreix

Coogan

2018

2018 IEEE Conference on Decision and Control (CDC)

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We derive an algorithm to compute satisfiability bounds for arbitrary ω-regular properties in an Interval-valued Markov Chain (IMC) interpreted in the adversarial sense. IMCs generalize regular Markov Chains by assigning a range of possible values to the transition probabilities between states. In particular, we expand the automata-based theory of ω-regular property verification in Markov Chains to apply it to IMCs.Any ω-regular property can be represented by a Deterministic Rabin Automata (DRA) with acceptance conditions expressed by Rabin pairs. Previous works on Markov Chains have shown that computing the probability of satisfying a given ω-regular property reduces to a reachability problem in the product between the Markov Chain and the corresponding DRA. We similarly define the notion of a product between an IMC and a DRA. Then, we show that in a product IMC, there exists a particular assignment of the transition values that generates a largest set of non-accepting states. Subsequently, we prove that a lower bound is found by solving a reachability problem in that refined version of the original product IMC. We derive a similar approach for computing a satisfiability upper bound in a product IMC with one Rabin pair. For product IMCs with more than one Rabin pair, we establish that computing a satisfiability upper bound is equivalent to lower-bounding the satisfiability of the complement of the original property. A search algorithm for finding the largest accepting and nonaccepting sets of states in a product IMC is proposed. Finally, we demonstrate our findings in a case study. arXiv:1809.06352v1 [cs.SY]

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“…These models have been extensively used in applications, including in robotics [4] and unmanned aircrafts [5]. Formal methods [6] are a means to verify the behavior of complex models against a rich set of specifications [7]. Linear temporal logic (LTL) is a particularly wellunderstood framework to express properties like safety, liveness, and priority [8], [9].…”

Section: Introductionmentioning

confidence: 99%

Secure Control under Partial Observability with Temporal Logic Constraints

Ramasubramanian

Clark

Bushnell

et al. 2019

2019 American Control Conference (ACC)

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This paper studies the synthesis of control policies for an agent that has to satisfy a temporal logic specification in a partially observable environment, in the presence of an adversary. The interaction of the agent (defender) with the adversary is modeled as a partially observable stochastic game. The search for policies is limited to over the space of finite state controllers, which leads to a tractable approach to determine policies. The goal is to generate a defender policy to maximize satisfaction of a given temporal logic specification under any adversary policy. We relate the satisfaction of the specification in terms of reaching (a subset of) recurrent states of a Markov chain. We then present a procedure to determine a set of defender and adversary finite state controllers of given sizes that will satisfy the temporal logic specification. We illustrate our approach with an example.

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Formal Verification and Synthesis for Discrete-Time Stochastic Systems

Cited by 123 publications

References 36 publications

StocHy - automated verification and synthesis of stochastic processes

StocHy - automated verification and synthesis of stochastic processes

Satisfiability Bounds for co-regular Properties in Interval-valued Markov Chains

Secure Control under Partial Observability with Temporal Logic Constraints

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